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On Banach spaces containing complemented and uncomplemented subspaces isomorphic to c\(_0\). (English) Zbl 1053.46004

Solving a problem from [S. A. Argyros, J. F. Castillo, A. S. Granero, M. Jiménez and J. P. Moreno, Proc. Lond. Math. Soc., III. Ser. 85, No. 3, 742–768 (2002; Zbl 1017.46011)], the authors present several examples of Banach spaces \(X\) such that every copy of \(c_0\) in \(X\) contains a further copy of \(c_0\) that is complemented in \(X\), yet not every copy of \(c_0\) in \(X\) is complemented.

MSC:

46B03 Isomorphic theory (including renorming) of Banach spaces
46B26 Nonseparable Banach spaces

Citations:

Zbl 1017.46011
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